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Apparently Scrooge was human experiment (doesn't say which group was doing it, but I'm guessing it's the one that Keido and Yuu were part of).

We know that Keido and Daath were trying to create an Eve for Mana and we know that Scrooge has a striking similarity with Shu. Maybe Scrooge was a clone of Shu, who Daath could use and control if Kurosu didn't comply with them and went rouge like Gai and the other Human Experiments. Same with Carol.

So with the last words in this trailer we can see it's connection with the anime?

It looks like they say something about Shu's dad, if you don't care, could you tell us what exactly was said about him?
(and if it isn't too much, a general idea of what the trailer said apart that Scrooge didn't know who is he at the start of the pv)

About last part of the preview - looks like it's dialog between Carol and Scrooge:
Carol: A-ah, he/she/it died. So? What are you going to do now?
Scrooge: It's decided. My next prey will be... Ouma Kurosu.

Official site updated with screenshots of the OVA and sample images of the alternate cover arts by redjuice and Hiromi Kato.

Short OVA summary: In the midst of their escape and revenge against Daath, Scrooge and Carol arrive at a port city where they get attached to a puppy. However they are pursued by a Sephiria Genomics unit lead by a young Segai.